Chapter 1.1, Problem 42E

Let the operation of addition be defined on subsets $A\text{and }B\text{of }U$ by $$ $A+B=\left(A\cup B\right)-\left(A\cap B\right)$. Use a Venn diagram with labelled regions to illustrate each of the following statements.

a. $A+B=\left(A-B\right)\cup \left(B-A\right)$

b. $A+\left(B+C\right)=\left(A+B\right)+C$

c. $A\cap \left(B+C\right)=\left(A\cap B\right)+\left(A\cap C\right)$.